Solving bilevel programs based on lower-level Mond-Weir duality

This paper focuses on developing effective algorithms for solving bilevel program. The most popular approach is to replace the lower-level problem by its Karush-Kuhn-Tucker conditions to generate a mathematical program with complementarity constraints (MPCC). However, MPCC does not satisfy the Mangasarian-Fromovitz constraint qualification (MFCQ) at any feasible point. In this paper, inspired by a recent work using the lower-level Wolfe duality (WDP), we apply the lower-level Mond-Weir duality to present a new reformulation, called MDP, for bilevel program. It is shown that, under mild assumptions, they are equivalent in globally or locally optimal sense. An example is given to show that, different from MPCC, MDP may satisfy the MFCQ at its feasible points. Relations among MDP, WDP, and MPCC are investigated. Furthermore, in order to compare the new MDP approach with the MPCC and WDP approaches, we design a procedure to generate 150 tested problems randomly and comprehensive numerical experiments showed that MDP has evident advantages over MPCC and WDP in terms of feasibility to the original bilevel programs, success efficiency, and average CPU time.Comment: arXiv admin note: text overlap with arXiv:2302.0683

A novel approach for bilevel programs based on Wolfe duality

This paper considers a bilevel program, which has many applications in practice. To develop effective numerical algorithms, it is generally necessary to transform the bilevel program into a single-level optimization problem. The most popular approach is to replace the lower-level program by its KKT conditions and then the bilevel program can be reformulated as a mathematical program with equilibrium constraints (MPEC for short). However, since the MPEC does not satisfy the Mangasarian-Fromovitz constraint qualification at any feasible point, the well-developed nonlinear programming theory cannot be applied to MPECs directly. In this paper, we apply the Wolfe duality to show that, under very mild conditions, the bilevel program is equivalent to a new single-level reformulation (WDP for short) in the globally and locally optimal sense. We give an example to show that, unlike the MPEC reformulation, WDP may satisfy the Mangasarian-Fromovitz constraint qualification at its feasible points. We give some properties of the WDP reformulation and the relations between the WDP and MPEC reformulations. We further propose a relaxation method for solving WDP and investigate its limiting behavior. Comprehensive numerical experiments indicate that, although solving WDP directly does not perform very well in our tests, the relaxation method based on the WDP reformulation is quite efficient

Service selection strategic analysis for selfoperated e-commerce platforms under settlement

In order to study whether e-commerce platforms carry out service cooperation after settlement in-depth, this paper focuses on service selection strategic analysis for agent channels on some self-operated e-commerce platforms settled in hybrid e-commerce platforms. We present multi-leader-follower models in two different scenarios with the platforms as leaders and the manufacturers as followers and give some numerical experiments to analyze the impacts of service selection strategies for self-operated platforms on all supply chain members. Our finding shows that if the service cost efficiency is moderate or low, the self-operated platform prefers to provide its service for the agent; otherwise, its selection mainly depends on the unit product service fee. In addition, fierce service competition and high unit service fee are unfavorable to all members, while high service cost efficiency may hurt both the platform and the manufacturer

Examination of expense and investment policy for centrally managed items in the Air Force and Navy

Approved for public release, distribution unlimitedMBA Professional ReportA basic principle of fiscal law is the identification of an object of expenditure as either an investment or expense; the identification then determines the proper appropriation and means through which the item is acquired. Part of the decision logic for an investment/expense determination is whether the items are centrally managed. The policies and practices surrounding central management of items varies across military departments and sometimes varies within a military department. This report documents various processes, as they exist today, and chronicles changes that occurred recently in the U.S. Air Force. Analyzing those processes indicates unclear policy direction, which leads to nonstandard implementation and problems with compliance. The presence of centralized information technology seems to lessen confusion and aid standardization of practices. Recommendations are offered for policy makers who may be considering changing policies

Interlayer motion and ultra-low sliding friction in microscale graphite flakes

The interlayer friction force $(F_{\mathrm{f}})$ of incommensurate graphite is a key material parameter to understand the mechanism of superlubricity and the unexpected properties of carbon-based materials; however, its determination by direct experiments under different ambient temperatures and sliding velocities is yet to be reported. In this letter, we report the direct, accurate experimental measurement of the $F_{\mathrm{f}}$ of microscale incommensurate graphite. The measured $F_{\mathrm{f}}$ per unit area, $F_{\mathrm{f}}=0.015\pm 0.008\ \text{MPa}$ in ambient laboratory conditions, decreases with increasing temperature $(22~^{\circ}\text{C}\le T \le 185~^{\circ}\text{C})$ , exhibits a logarithmic increase with respect to sliding velocities $(40\ \text{nm/s}\le v \le 12000\ \text{nm/s})$ and remains almost unchanged under various twist angles. At elevated temperatures, $F_{\mathrm{f}}$ can be lower than the resolution of the force sensor, which corresponds to $F_{\mathrm{f}}=0.32\ \text{kPa}$ per unit area. This is the lowest value reported for lamellar materials. These experimental measurements assist in understanding the mechanism of microscale superlubricity and such an ultra-low friction force will also introduce a wide range of applications in microelectromechanical systems (MEMS)

Rigid–Flexible Contact Analysis of an Inflated Membrane Balloon with Various Contact Conditions

Considering the Mooney–Rivlin hyperelastic model, a semi-analytical approach is introduced to analyze the rigid–flexible contact behavior of an inflated membrane balloon between two plates with various interface conditions. This approach is based on differential formulation, and the coupling properties of equilibrium equations are well-solved. In order to verify the reliability of the proposed theoretical model, an experimental test was designed, by which some important contact characteristics and patterns (no-slip condition) were obtained. Two special phenomena were observed for the meridian stretch ratio with different friction coefficients. One is that the intersection points of all curves fall in a small interval, and the intersection of any two curves represents the same changing rate of the horizontal ordinate, resulting in the maximum difference. The other is the dividing point, where the stretch ratio decreases on the left and increases on the right due to the introduction of friction. These results provide solid guidance and support for our understanding of the rigid–flexible contact behavior of inflated membrane balloons

Sensing Performance Analysis on Quartz Tuning Fork-Probe at the High Order Vibration Mode for Multi-Frequency Scanning Probe Microscopy

Multi-frequency scanning near-field optical microscopy, based on a quartz tuning fork-probe (QTF-p) sensor using the first two orders of in-plane bending symmetrical vibration modes, has recently been developed. This method can simultaneously achieve positional feedback (based on the 1st in-plane mode called the low mode) and detect near-field optically induced forces (based on the 2nd in-plane mode called the high mode). Particularly, the high mode sensing performance of the QTF-p is an important issue for characterizing the tip-sample interactions and achieving higher resolution microscopic imaging but the related researches are insufficient. Here, we investigate the vibration performance of QTF-p at high mode based on the experiment and finite element method. The frequency spectrum characteristics are obtained by our homemade laser Doppler vibrometer system. The effects of the properties of the connecting glue layer and the probe features on the dynamic response of the QTF-p sensor at the high mode are investigated for optimization design. Finally, compared with the low mode, an obvious improvement of quality factor, of almost 50%, is obtained at the high mode. Meanwhile, the QTF-p sensor has a high force sensing sensitivity and a large sensing range at the high mode, indicating a broad application prospect for force sensing